# How do you factor completely #a^2 - 2ab - 15b^2#?

##### 1 Answer

Apr 18, 2016

#### Explanation:

Since this is a homogeneous polynomial of degree

Find a pair of factors of

#a^2-2ab-15b^2 = (a-5b)(a+3b)#

Alternatively, you can complete the square and use the difference of squares identity:

#A^2-B^2=(A-B)(A+B)#

with

#a^2-2ab-15b^2#

#=(a-b)^2-b^2-15b^2#

#=(a-b)^2-(4b)^2#

#=((a-b)-4b)((a-b)+4b)#

#=(a-5b)(a+3b)#